Ultralow thermal expansion in Ge-based o-MAX phases enabled by multicomponent alloying and bonding network reconstruction

Out-of-plane chemical ordering in 413-type Ge-based MAX phases has recently been identified, establishing the second known series of o-MAX phases. However, the evolution of their bonding characteristics and intrinsic thermal expansion with chemical composition remains unclear. Here, we systematically investigate the thermal expansion behavior and stability of 413-type Ge-based o-MAX phases. Results demonstrate that the dilation of the M–A bond contributes dominantly to the thermal expansion, increasing the n-value (MX-layer thickness) in Ge-based MAX phases, effectively reducing the average coefficient of thermal expansion (CTE). Remarkably, the quaternary (CrTiVMo)GeC₃ exhibits an ultralow CTE of 3.77(1) μK⁻¹ over 298–1073 K, which is the lowest reported among all MAX phases with excellent thermal stability. Bond-length dilation analysis reveals that the ultra-low CTE arises from a dramatic suppression of the thermal expansion of specific bonds, most notably the interlayer M−Ge and intra-layer M−X bonds. Grüneisen parameter analysis links this ultralow expansion to a significantly suppressed lattice anharmonicity (γ ≈ 1.15). Mechanistically, bond order analysis reveals that this suppression originates from a synergistically reconstructed bonding network due to V/Mo co-doping, wherein Mo acts as a strong bond former, and V provides a crucial optimizing effect, together producing a systematic increase in bond orders, particularly for interlayer M−Ge bonds. These findings establish multicomponent alloying in ordered nanolaminates as a powerful route to materials with tailored thermal expansion for extreme environments.